Final answer:
The elevation gain of Lars' chairlift ride, with a 37° incline and a path length of 1,392 m, is approximately 840 m, which is option (a).
Step-by-step explanation:
Lars is riding a chairlift that rises at a constant angle of 37°, and the length of the chairlift ride is 1,392 m. To find the elevation gain from the base of the chairlift to the top, we need to use trigonometry, specifically the sine function which relates the length of the hypotenuse of a right triangle (the chairlift path) to the length of the opposite side (the elevation gain).
The sine of an angle in a right triangle is equal to the opposite side divided by the hypotenuse. In mathematical terms, this is expressed as:
sin(θ) = opposite / hypotenuse
Therefore, to find the opposite side, we can rearrange the formula:
opposite = hypotenuse × sin(θ)
Plugging in the numbers:
opposite = 1,392 m × sin(37°)
Using a calculator to find the sine of 37 degrees and multiplying it by 1,392 gives us the opposite side, which is the elevation gain:
opposite = 1,392 m × 0.6018 ≈ 837.86 m
Thus, the elevation gain is approximately 840 m, which corresponds to option (a).